1. Field of the Invention
The invention relates to digital devices for performing rotation of an arbitrary input. In particular, the invention relates to circuit and methods for reducing the complexity and power dissipation in physical circuits that perform angle rotation.
2. Related Art
An angle rotator performs the conceptually straightforward operation of rotating an arbitrary point (X0, Y0) in the X-Y plane, counter-clockwise, about the origin in the plane, through a given angle θ. A digital angle rotator performs such rotations on data points whose coordinate values are specified by digital data words. It can also be insightful to view the rotation operation as a rotation of a complex number X0+jY0 in the complex plane. The digital angle rotator may be used to implement a digital modulator or a digital mixer in a communication system, as well as for implementing angle-rotation operations for other popular signal-processing systems, such as, but not limited to, discrete Fourier transformers and/or trigonometric interpolators to provide some examples.
The digital angle rotator differs significantly from a traditional digital mixer that employs an interconnection of two subsystems: a direct digital frequency synthesizer (DDFS) and a complex multiplier. Crucial insight into the digital angle rotator derives from the observation that the multiplication of an input complex number by a special complex number, one having the form cos θ+j sin θ, is a more special operation than simply the multiplication of two arbitrary complex numbers. Namely this is the multiplication of an arbitrary complex-number by a complex number having magnitude one, making the complex multiplication become a counter-clockwise rotation of an input complex number, about the origin in the complex plane, through the angle θ. The complexity of a conventional angle rotator is approximately the same as that of the multiplier block alone in the traditional digital mixer implementation. Therefore, what is needed is an angle rotator that is reduced in complexity and power dissipation as compared to the conventional prior-art angle rotator.
The present invention will now be described with reference to the accompanying drawings. In the drawings, like reference numbers generally indicate identical, functionally similar, and/or structurally similar elements. The drawing in which an element first appears is indicated by the leftmost digit(s) in the reference number.